Theory:

A set of numbers is said to be associative for a specific mathematical operation if the result obtained when changing grouping (parenthesizing) of the operands does not change the result.
Whole Numbers:
i) Addition: Changing the grouping of operands in addition to whole numbers, does not change the result. Hence, whole numbers under addition are associative.

2 + (3 + 6) = (2 + 3) + 6(0 + 6)+ 8 = 0 + (6 + 8)

ii) Subtraction: Changing the grouping of operands in the subtraction of whole numbers changes the result. Hence, whole numbers under subtraction are not associative.
 
5 − (3 − 4) ≠ (5 − 3) − 4(2 − 0) − 6 ≠ 2 − (0 − 6)

iii) Multiplication: Changing the grouping of operands in the multiplication of whole numbers does not change the result. Hence, whole numbers under multiplication are associative.
 
5 × (3 × 6) = (5 ×3× 6(2 × 0)× 9 = 2 × (0 × 9)

iv) Division
: Changing the grouping of operands in the division of whole numbers changes the result. Hence, whole numbers under division are not associative.

4 ÷ (2 ÷ 6) ≠(4 ÷ 2) ÷ 6(10 ÷ 4)÷ 7 ≠10 ÷ (4 ÷ 7)
Integers:
i) Addition: Changing the grouping of operands in addition to integers, does not change the result. Hence integers under addition are associative.

2 + (3 + (−6)) = (2 + 3) + (−6)(0 + (−6)) + (−8) = 0 + ((−6) + (−8))

ii) Subtraction: Changing the grouping of operands in the subtraction of integers changes the result. Hence, integers under subtraction are not associative.

5 − (3 − (−4)) ≠ (5 − 3) − (−4)((−2) − 0) − 6 ≠ (−2) − (0 − 6)

iii) Multiplication: Changing the grouping of operands in the multiplication of integers does not change the result. Hence, integers under multiplication are associative.
 
5 × ((−3× 6) = (5 × (−3)) × 6((−2× 0)× (−9)= (−2)× (0 × (−9))

iv) Division: Changing the grouping of operands in the division of integers changes the result. Hence, integers under division are not associative.

4 ÷ (2 ÷(6)) ≠(4 ÷ 2) ÷(6)((10) ÷ 4) ÷ 7 ≠(10) ÷ (4 ÷ 7)
Rational Numbers:
i) Addition: Changing the grouping of operands in addition to rational numbers, does not change the result. Hence, rational numbers under addition are associative.
 
ab+cd+ef=ab+cd+ef

23+32+ (6)7 =23+32+ (6)7

ii) Subtraction: Changing the grouping of operands in the subtraction of rational numbers changes the result. Hence, rational numbers under subtraction are not associative.
 
abcdef=abcdef
 
2332(6)72332(6)7

iii) Multiplication: Changing the grouping of operands in the multiplication of rational numbers does not change the result. Hence, rational numbers under multiplication are associative.
 
ab×cd×ef=ab×cd+ef
 
23×32×(6)7=23×32×(6)7

iv) Division: Changing the grouping of operands in the division of rational numbers changes the result. Hence, rational numbers under division are not associative.
 
ab÷cd÷ef=ab÷cd÷ef
 
23÷32÷(6)7=23÷32÷(6)7